If the areas of two similar triangles are equal, prove that they are congruent

Answer:

76 degrees

Step-by-step explanation:

Let the angles be x, y and z

As per given:

Considering the first 2 equations in the third one:

So the third angle is:

Answer:

30.9 cm²

Step-by-step explanation:

To find the surface area of this figure, we find the area of the base and the 3 identical sides.

The base is split into two identical right triangles. Let's find the area of one and multiply by two.

Half of 3: 1.5

[tex]1.5\cdot2.6=3.9\\3.9\div2=1.95[/tex]

There are two right triangles:

[tex]1.95\cdot2=3.9[/tex]

The area of one of the sides will be the same thing, except the height is 6.

[tex]1.5\cdot6=9\\9\div2=4.5\\4.5\cdot2=9[/tex]

There are 3 sides identical to this one:

[tex]9\cdot3=27[/tex].

Add 27 and 3.9:

[tex]27+3.9=30.9[/tex]

Hope this helped!

Answer:

30.9 square centimeters

Step-by-step explanation:

3 * 1/2(3)(6) + 1/2(3)(2.6) = 30.9

Step-by-step explanation: The first rectangle to the right is 24 because 10+14 equals 24. The rectangle to the left is 19 because 10+9 equals 19. Finally the rectangle on the bottom is 23 because 14+9 is 23

Answer:

f(x) = 4sin(x) - 3

Step-by-step explanation:

Answer:

1533

Step-by-step explanation:

73x21= 1533

Answer:

73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73

=73x21=1533

Step-by-step explanation:

Answer:

The answer to your question is 7 lbs.

Step-by-step explanation:

Data

angle = 70°

force = 20 lb

horizontal component

Process

To solve this problem just imagine a right triangle, where the force is the hypotenuse and the horizontal component is the adjacent side.

1.- Look for a trigonometric function that relates the adjacent side and the hypotenuse.

                  cos Ф = adjacent side / hypotenuse

- Solve for the adjacent side

                  adjacent side = hypotenuse x cosФ

- Substitution

                  adjacent side = 20 x cos 70

- Simplification

                  adjacent side = 20 x 0.342

- Result

                  adjacent side = 6.84 ≈ 7 lb  

Step-by-step explanation:

x+3/x-2-1-x/x=17/4find the LCM of the denominators (x-2)x=x^2-2x

(x^2-2x)4=4x^2-8x divide the denominator by the LCM and then multiply x to the numerator

(x+3)4=4×+3

(1-x)(4x-8)

1(4x-8)-x(4x-8)

4x-8-4x^2-8x=4x

Answer:

umm it's a piecewise function and I think the graph is correct I don't really understand what you mean by what is the "graph" of the following function since the graph is already there...

Step-by-step explanation:

Answer:  D. (-2, -1)

Step-by-step explanation:

Here we do two reflections to the point (-1, 2).

First, we do a reflection over the line x = y.  Remember that a reflection over a line keeps constant the distance between our point and the given line, so we have that for a pint (x, y), the reflection over the line y = x is:

Ry=x (x, y) = (y, x)

so for our point, we have:

Ry=x (-1, 2) = (2, -1)

Now we do a reflection over the y-axis, again, a reflection over a line keeps constant the distance between our point and the given line, so if we have a point (x,y) and we do a reflection over the y-axis, our new point will be:

Ry-axis (x,y) = (-x, y)

Then in our case:

Ry-axis (2, -1) = (-2, -1)

The correct option is D.

Answer:

AE = 18 units

Step-by-step explanation:

Δ AEB and Δ DEC are similar , then corresponding sides are in proportion, that is

[tex]\frac{AE}{DE}[/tex] = [tex]\frac{AB}{DC}[/tex] , substitute values

[tex]\frac{2x+4}{x+8}[/tex] = [tex]\frac{12}{10}[/tex] ( cross- multiply )

10(2x + 4) = 12(x + 8) ← distribute parenthesis on both sides

20x + 40 = 12x + 96 ( subtract 12x from both sides )

8x + 40 = 96 ( subtract 40 from both sides )

8x = 56 ( divide both sides by 8 )

x = 7

Then

AE = 2x + 4 = 2(7) + 4 = 14 + 4 = 18 units

Answer:

135

Step-by-step explanation:

The equation is 135+90+x=360. x=360-(225)=135

Answer: 1/4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

=(-5)+(-10)+(-9)/2*(-3)

=-5-10-9/-6

=-24/-6

=4 ans.....

Answer:

division involves 5 steps:

D Divide

M Multiply

S Subtract

B Bring down

R Repeat or Remainder

Step-by-step explanation: i hope it helped

Answer:

Area= 452.23 ft²

Step-by-step explanation:

Angle at U = 180-48-20

Angle at U = 112°

UT/sin 112=46/sin 48

UT= 0.9272*46/0.7431

UT=57.4 ft

UV= sin 20*46/sin48

UV= 0.3420*46/0.7431

UV= 21.2 ft

S=( 21.2+57.4+46)/2

S=124.6/2

S= 62.3

Area= √((62.3)(62.3-21.2)(62.3-57.4)(62.3-46))

Area= √((62.3)(41.1)(4.9)(16.3))

Area= √204509.5311

Area= 452.23 ft²

Answer:

$10.48

Step-by-step explanation:

To the nearest cent, your answer would be 10.48

Answer:

2

Step-by-step explanation:

because ther is in the picture

Answer:

-1

Step-by-step explanation:

3/2 * (-22/33)

Simplify by dividing the second fraction by 11

3/2 * (-2/3)

Rewriting

3/3 * (-2/2)

-1/1

Answer:

-1

Step-by-step explanation:

(a/b)(c/d) = (a*c)(

(3/2)(-22/33)

(3*-22)/(2*33) = -66/66 = -1

Answer:

[tex]\Large \boxed{11.08}[/tex]

Step-by-step explanation:

The triangles are congruent, we can use ratios to solve.

AD/DC = BE/EC

Let the length of EC be x.

6/14 = 4.75/x

Solve for x.

Cross multiply.

6 × x = 14 × 4.75

6x = 66.5

Divide both sides by 6.

(6x)/6 = (66.5)/6

x = 11.083333...

Greetings from Brasil...

Here we can use similarities of triangles

AC/DC = BC/EC

20/14 = (4.75 + X)/X

X ≅ 11.1

see attachment

Answer:

[tex]\displaystyle x=\left \{\frac{2\pi}{3}+2\pi k,\frac{4\pi}{3}+2\pi k, \frac{8\pi}{3}+2\pi k, \frac{10\pi}{3}+2\pi k\right \}k\in \mathbb{Z}[/tex]

Step-by-step explanation:

Hi there!

We want to solve for [tex]x[/tex] in:

[tex]4\sin^2(\frac{x}{2})=3[/tex]

Since [tex]x[/tex] is in the argument of [tex]\sin^2[/tex], let's first isolate [tex]\sin^2[/tex] by dividing both sides by 4:

[tex]\displaystyle \sin^2\left(\frac{x}{2}\right)=\frac{3}{4}[/tex]

Next, recall that [tex]\sin^2x[/tex] is just shorthand notation for [tex](\sin x)^2[/tex]. Therefore, take the square root of both sides:

[tex]\displaystyle \sqrt{\sin^2\left(\frac{x}{2}\right)}=\sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}}[/tex]

Simplify using [tex]\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}[/tex]:

[tex]\displaystyle \sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \frac{\sqrt{3}}{\sqrt{4}}=\pm \frac{\sqrt{3}}{2}[/tex]

Let [tex]\phi = \frac{x}{2}[/tex].

[tex]\displaystyle \sin(\phi)=\frac{\sqrt{3}}{2},\\\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}[/tex]

Therefore, we have:

[tex]\displaystyle \frac{x}{2}=\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\frac{x}{2}=\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z},\\\\\begin{cases}x=\boxed{\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{4\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}[/tex]

[tex]\displaystyle \sin(\phi)=-\frac{\sqrt{3}}{2},\\\phi = \frac{4\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{5\pi}{3}+2\pi k, k\in \mathbb{Z},\\\begin{cases}x=\boxed{\frac{8\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{10\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}[/tex]

Answer:

Step-by-step explanation:

- 2(5y - 1) - y = - 4(y - 3)

Expand the terms in the bracket

That's

-10y + 2 - y = - 4y + 12

Group like terms

Send the constants to the right side of the equation and those with variables to the left side

That's

- 10y - y + 4y = 12 - 2

- 7y = 10

Divide both sides by - 7

We have the final answer as

Hope this helps you

Answer:

The distribution is positively skewed.

Step-by-step explanation:

It's not symmetric because the distribution in the chart isn't equally shown or marked. It's not negative skewed either because for it to be negative the graph would have to go down in a negative direction, usually the left, but in the picture you posted the graph is going down in the right direction. Lastly, positively skewed graphs or charts look like the one you posted. They go down in the right direction, hence why they're called "positively" skewed. The right tail of the distribution is longer in positively skewed graphs or charts.

Answer:

31.5cm²

Step-by-step explanation:

area of a triangle =1/2 b h

b= 7cm

h=9cm

1/2×7×9

= 1/2×63

= 31.5cm²

hypotenuse is unknown so,

c²=a²+b²

c²= 7² + 9²

= 49 + 81

c²= 130

c= 11.4cm

perimeter= 7 +9+11.4

=27.4cm

pls note that no unit was stated

Answer:

answer is 90°

Step-by-step explanation:

it's simple , these both angles are complementary so sum of both is 90°

I hope it helped:)

Answer:

see below

Step-by-step explanation:

58+32 = 90

The angles add to 90 degrees, so the angles are complementary

Answer:

6x + 3 + 2y

Step-by-step explanation:

The GCF is 6 as thats the largest factor, so you divide the numbers by 6.

6x + 3 + 2y

Answer:

The choose C. 2

Step-by-step explanation:

[tex]slope = \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 2 + 4}{3 - 2} = \frac{2}{1} = 2[/tex]

Answer:

option C is correct

Step-by-step explanation:

Hope it is helpful....

Answer:

When two inscribed angles in one circle both equal 75°, the two angles must intercept the same arc that measures 75°

Step-by-step explanation:

Based on the Inscribed Angles Theorem, the measure of an intercepted arc is twice the measure of the inscribed angle that intercepts it in a circle.

Consequently, the theorem also Holds that the measure of two inscribed angles intercepting the same arc, are congruent. In other words, both angles together are the same, and their sum would give you the measure of the arc they both intercept.

In the diagram shown in the attachment below, we have 2 inscribed angles, angle A and B. They both intercept the same arc of 75°.

Therefore, we can conclude that the measure of both angles equal 75°, which is the same as the measure of the arc they intercept.

Angle A = Angle B

m<A + m<B = measure of intercepted arc = 75°

Answer: the answer is P

Step-by-step explanation:

Answer:

95%

Step by step explanation:

z = 17-21 / 2 and z = 25-21/2

z=-2 (2.28%) z=2 (97.72%)

97.72 - 2.28 = 5.44

100% - 5.44% is about equal to 95%

Answer:

488

Step-by-step explanation: